I noticed that Shapeways had 13 models of the roundest of the fullerenes (one of the 1812 forms of C60), but none of the less regular forms; so I made some.

Each of the white pieces has mirror symmetry; the red pieces are chiral. Not shown (because it hasn’t been printed yet): the blue set, which is a reflection of the red set. The idea is that you buy both red and blue if and only if you count reflected chiral forms separately.

These figures have 12 pentagons and up to 8 hexagons. They include the two smallest forms with no nontrivial symmetries, and the two smallest with no ‘peaks’ where three pentagons meet.

Shapeways has thirteen models of (the most symmetrical and famous form of) C60, but none of the thousands of smaller fullerenes. So I designed models of the 35 smallest, i.e. up to C36; this includes the smallest with no symmetries, and the smallest with no ‘peaks’ where three pentagons meet. One bundle has the 19 forms with mirror symmetry; two other bundles will have the 16 or 32 chiral forms (arbitrarily divided), so that the buyer can choose to have both or only one of a pair distinguished only by handedness.

I’ll make them available when I have them in my hands and am satisfied of their strength.

A new father asked:

Are you charmed or annoyed to learn that your 3d geometric object is making a great toy for [baby, 8 mo.]?

I replied:

I have cats, so I’m not a bit surprised!

On a related note, if I had any knowledge of Web programming I’d make something analogous to this.

This one is a projection of a design on (half of) the surface of a hypersphere: a ribbon spans two orthogonal great circles, wrapping three times around one and five times around the other.

Kitty teeth did break it at one point, but with redundancy that’s not a serious problem. Having got my pix I’ll keep the new toys away from them henceforth.

Not only did it not fall apart in my hands …

The strand — for it is a Klein bottle woven of a single strand — is thinner than I expected, and has broken in at least two places. Ah well, live and learn; I’ve already redesigned it to be more robust.

I submitted a design to Shapeways today! I’ll tell you more if it doesn’t fall apart when I get it in my hands.